BENDING ANALYSIS OF TAPERED EULER-BERNOULLI BEAM OF AXIALLY FUNCTIONALLY GRADED BI-MODULUS MATERIAL


Hacıoğlu A., Baykara C.

6. INTERNATIONAL MARMARA SCIENTIFIC RESEARCH AND INNOVATION CONGRESS, İstanbul, Turkey, 7 - 08 October 2023, pp.512-524

  • Publication Type: Conference Paper / Full Text
  • City: İstanbul
  • Country: Turkey
  • Page Numbers: pp.512-524
  • Recep Tayyip Erdoğan University Affiliated: Yes

Abstract

This study investigates the bending behavior of a tapered Euler-Bernoulli beam featuring a Ludwick-type non-linearly elastic material with bi-modulus properties and axial functional gradation. The material composition of the functionally graded beam exhibits axial variation following the Voigt model and Power Law. Notably, the constitutive relation of the material is Ludwick-type non-linear, characterized by distinct behaviors in tensile and compressive domains. In response to both material non-linearity and geometric non-linearity, an algorithm has been developed for numerical problem-solving employing the fourth-order Runge-Kutta method. The results emphasize that, in accordance with Euler-Bernoulli's kinematic relations, the maximum normal stresses occur at the upper and lower surfaces of the beam, regardless of the material and geometric parameters. However, it is noteworthy that the point of maximum tension and compression may vary across different cross-sections of the beam, depending on the aspect ratio of the structure. Furthermore, the bi-modulus property of the material leads to asymmetric expansion of the tensile and compressive domains along the length of the beam. Additionally, the material composition and aspect ratio exert a substantial influence on the deflection characteristics of the beam. This investigation sheds light on the intricate interplay between material composition, geometry, and mechanical behavior, offering insights into the analysis of axially functionally graded bi-modulus beams.